# Cyclic pentagons and hexagons with integer sides, diagonals and areas

## TL;DR

This paper constructs cyclic pentagons and hexagons with rational sides, diagonals, and areas, providing explicit formulas and methods to scale them to integer values, advancing the understanding of rational cyclic polygons.

## Contribution

It introduces a systematic way to generate cyclic pentagons and hexagons with rational and integer sides, diagonals, and areas using rational functions and scaling techniques.

## Key findings

- Explicit formulas for rational sides, diagonals, and areas.
- Methods to scale rational polygons to integer-sided ones.
- Construction of infinite families of such polygons.

## Abstract

In this paper we obtain cyclic pentagons and hexagons with rational sides, diagonals and area all of which are expressed in terms of rational functions of several arbitrary rational parameters. On suitable scaling, we obtain cyclic pentagons and hexagons whose sides, diagonals and area are all given by integers.